Up front, the game really doesn’t go into a lot of explicit details here. Just tempering your expectations now.
Second, “precise” damage here is a red herring: it’s irrelevant whether the damage is precision damage or not. Any generic damage bonus that doesn’t specify the bonus damage’s type has the same problem—this is exactly as much of a problem for smite evil (which is not precision damage) as it is for sneak attack (which is).
Third, the rules never actually let you just choose to touch someone for your attack, much less choose to do it with a weapon, so your entire flaming frost short sword maneuver isn’t a thing you can actually do. The assumption that flaming and frost would deal their damage if you could do that is invalid, too: since the rules don’t let you do that, the rest of the rules don’t consider the possibility of you doing that, and weren’t written to handle that as a possibility. Even if you houserule that someone can use one of their attacks to touch someone, and resolve it as a touch attack, and even if you allow them to do the touching with a weapon rather than just their hand—all entirely reasonable houserules—at that point you’ve changed something fundamental about the game and you can’t just rely on the rules that were written for resolving the effects of things like flaming, frost, or sneak attack: those were written assuming you can’t do this, so whether or not they work with this houseruled touch attack is a part of that houserule, not the official rules.
For the record, all of the actual official ways to do this kind of touch attack—such as groping around for an unseen assailant, or the combat rhythm tactical option from the Stormguard Warrior feat—state that these touch attacks “deal no damage.” That would nix the damage from sneak attack, flaming, and frost, making the question moot. That’s probably how you should rule things for any homebrewed generic touch attack option.
If you were to make a regular attack with the flaming frost short sword, things are easier. Flaming applies 1d6 bonus fire damage, frost applies 1d6 bonus cold damage, and the short sword itself deals 1d6 piercing damage. Sneak attack adds some amount of bonus damage—but the piercing damage is the attack’s “damage,” while the fire damage and cold damage are both other bonuses. Bonus damage extends the base damage, not other bonuses—this is not a bonus-on-a-bonus situation. The sneak attack damage is piercing.
Meteor swarm is a similar situation: the ranged touch attack you make deals 2d6 bludgeoning damage. It also triggers a blast of fire damage in an area (and denies the original target a Reflex saving throw), but that triggered blast of damage is not the damage of the ranged touch attack itself that you’re applying sneak attack to. Thus the sneak attack damage is bludgeoning. The fire damage is area damage that sneak attack doesn’t apply to.
